return is equal to 52%, which corresponds with a mean yearly excess return of 40%. The Sharpe ratio is equal to 0.1461 and the excess Sharpe ratio is equal to 0.1349. These excess performance measures are considerably large. The maximum loss of the strategy is 18.7%, half less than the maximum loss of buying and holding the MSCI World Index, which is equal to 38.7%. The number of trades is very large, once every 2.4 days, but also the percentage of profitable trades is very large, namely 74.8%. These profitable trades span 86% of the total number of trading days. Similar good results are also found for the other stock market indices. For 42 of the 51 indices the maximum loss of the best strategy is less than the largest cumulative loss of the buy-and-hold strategy. For most indices the percentage of profitable trades is larger than 70% and these profitable trades span more than 80% of the total number of trading days. Although the Sharpe ratio of the buy-and-hold was negative for 23 indices, indicating that these indices were not able in beating a continuous risk free investment, it is found for all indices that the best-selected strategy shows a positive Sharpe ratio.
If transaction costs are increased to 0.25% per trade, then table 5.4 shows that the best-selected strategies are strategies which generate substantially fewer signals in comparison with the zero transaction costs case. Trading positions are now held for a longer period. For example, the best strategy found for the MSCI World Index is a single crossover moving-average rule which generates signals if the price series crosses a 200-day moving average and where the single refinement is a 2.5%-band filter. This strategy generates a trade every 13 months. However due to transaction costs the performance of the technical trading rules decreases and also the percentage of profitable trades and the percentage of days profitable trades last decreases for most indices in comparison with the zero transaction costs case. However for all indices, the Sharpe ratio of the best strategy is still positive. This continues to be the case even if costs are increased to 1% per trade. Similar results are found for the two other trading cases.